Aye, the Pro license does cover systems of play and tactical application etc, but it's only one small part of a very holistic approach to management. You spend time on communication, the financial side of the game, a lot of time on training drills, recruitment,marketing, prep work, managing staff, physical conditioning, and plenty more. So while the top badge gives a brilliant insight into managing a club (and it does cover tactical theory and application), it's not necessarily going to turn you into Sacchi.
The coach argument is fair, but the first point I don't agree with. On the pitch and off the pitch is such a different world that being a more intelligent player doesn't necessarily translate into having a better tactical insight. While I don't think Neville is anything special, Keane has never shown any insight as a pundit. He might have a far better understanding than Neville, but it doesn't mean much if he doesn't share it. At least as a pundit.